22
2.2 The abstract structure of measurement
Measurement can be considered, preliminarily and in a general sense, to be a process based on empirical interaction with an object and aimed at producing information on a property of that object in the form of values of that property.
5,6,7
This characterization is generic: it provides conditions that are deemed to be
necessary but not also sufficient. In fact, not every such process is a measurement,
and several other definitions have been proposed that add empirical constraints on
the process and/or formal constraints on the entities considered to be measurable
(see the critical review in Chap. 4 and Mari, 2013). Nevertheless, some key features
of measurement are already inherent in this characterization: we introduce them
here with a step-by-step, top-down strategy, by imposing more and more constraints
and therefore progressively specifying the scope of measurement, in terms of the
following four black box conditions.
Measurement:
• is an empirical process (Sect. 2.2.1),
• designed on purpose (Sect. 2.2.2),
• whose input is a property of an object (Sect. 2.2.3), and
• that produces information in the form of values of that property (Sect. 2.2.4).
5 Compare this to the more specific definition of in the VIM: “process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity”
(JCGM, 2012: 2.1). Our use of the indefinite article “a” rather than the definite article “the” (“a
process …”, not “the process …”) emphasizes that in this chapter we introduce necessary but not
sufficient conditions to characterize measurement.
6 In this characterization the term “object” is used in a broad sense and refers to what the VIM calls
a “phenomenon, body, or substance” (for example in JCGM, 2012: 1.1) but also to an individual,
an organization, a process, etc. There is no claim that an object, in this sense, is a single, unitary
entity, and instead it may be a system, or even a conglomerate, of parts. Furthermore, “object” is
ambiguous, given that in semiotics an object is meant to be an object of the discourse and therefore
properties are, in this sense, objects. Without any further specific ontological commitment, here we
consider an object to be anything that bears properties; in Chaps. 5 and 6 we develop a more analytical consideration of properties.
7 The term “value” is ambiguous. In particular, a phrase such as “to be of little value to somebody”
shows that it can be used, as an uncountable, for, as
mentioned in the Oxford English Dictionary. In measurement science, and in this book, “value”
has a meaning analogous to what in mathematics is (so that,
for example, 1 is the value of the function cos(x) when applied to the argument x = 0), thus devoid
of any ethical or axiological components. However, an ambiguity remains: if X is a variable ranging over a set {x i }, each x i is said to be a value of X; hence by modeling a property, such as mass or
shape, as a variable, each of its instances, such as a given mass and a given shape, would be considered to be a value of that variable. As we discuss in the following pages, and further in Chap. 6,
in the tradition of measurement science the term “value of a property/quantity” is reserved for the
instances of properties/quantities that are identified as elements of a classification, which in the
case of quantities is induced by the appropriate composition of a quantity chosen as the unit.
2 Fundamental concepts in measurement
2.2 The abstract structure of measurement
Measurement can be considered, preliminarily and in a general sense, to be a process based on empirical interaction with an object and aimed at producing information on a property of that object in the form of values of that property.
5,6,7
This characterization is generic: it provides conditions that are deemed to be
necessary but not also sufficient. In fact, not every such process is a measurement,
and several other definitions have been proposed that add empirical constraints on
the process and/or formal constraints on the entities considered to be measurable
(see the critical review in Chap. 4 and Mari, 2013). Nevertheless, some key features
of measurement are already inherent in this characterization: we introduce them
here with a step-by-step, top-down strategy, by imposing more and more constraints
and therefore progressively specifying the scope of measurement, in terms of the
following four black box conditions.
Measurement:
• is an empirical process (Sect. 2.2.1),
• designed on purpose (Sect. 2.2.2),
• whose input is a property of an object (Sect. 2.2.3), and
• that produces information in the form of values of that property (Sect. 2.2.4).
5 Compare this to the more specific definition of
(JCGM, 2012: 2.1). Our use of the indefinite article “a” rather than the definite article “the” (“a
process …”, not “the process …”) emphasizes that in this chapter we introduce necessary but not
sufficient conditions to characterize measurement.
6 In this characterization the term “object” is used in a broad sense and refers to what the VIM calls
a “phenomenon, body, or substance” (for example in JCGM, 2012: 1.1) but also to an individual,
an organization, a process, etc. There is no claim that an object, in this sense, is a single, unitary
entity, and instead it may be a system, or even a conglomerate, of parts. Furthermore, “object” is
ambiguous, given that in semiotics an object is meant to be an object of the discourse and therefore
properties are, in this sense, objects. Without any further specific ontological commitment, here we
consider an object to be anything that bears properties; in Chaps. 5 and 6 we develop a more analytical consideration of properties.
7 The term “value” is ambiguous. In particular, a phrase such as “to be of little value to somebody”
shows that it can be used, as an uncountable, for
mentioned in the Oxford English Dictionary. In measurement science, and in this book, “value”
has a meaning analogous to what in mathematics is
for example, 1 is the value of the function cos(x) when applied to the argument x = 0), thus devoid
of any ethical or axiological components. However, an ambiguity remains: if X is a variable ranging over a set {x i }, each x i is said to be a value of X; hence by modeling a property, such as mass or
shape, as a variable, each of its instances, such as a given mass and a given shape, would be considered to be a value of that variable. As we discuss in the following pages, and further in Chap. 6,
in the tradition of measurement science the term “value of a property/quantity” is reserved for the
instances of properties/quantities that are identified as elements of a classification, which in the
case of quantities is induced by the appropriate composition of a quantity chosen as the unit.
2 Fundamental concepts in measurement